arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 1110.0643math.LO
收藏

不可及性和次不可及性。分为两部分。部分II(俄文)

Inaccessibility and subinaccessibility. In two parts. Part II (in Russian)

Alexander Kiselev

摘要:

这项工作是从英文翻译成俄文的第二部分的专着亚历山大基谢廖夫在同一标题。它包含证明(在ZF)的不可达基数不存在。这部作品的第一版于2000年出版。这第二部分包含应用subaccessible红衣主教的设备和它的基本工具-理论的减少公式谱和矩阵,传播者和其他人,这是在这里使用的证明,并提出了现在在其更透明和完善的形式。许多注意力都集中在更明确和实质性的发展和基本思想的培养,作为所有主要建设和推理的基础。详细地给出了关于不可达基数不存在性定理的证明。给出了这个定理的几个简单的推论和一些著名的结果。适用于集合论和数理逻辑专家,以及数学专业的教师和学生。

英文摘要:

This work represents a translation from English into Russian of the second part of the monograph by Alexander Kiselev under the same title. It contains the proof (in ZF) of inaccessible cardinals nonexistence. The first edition of this work was published in 2000. This part II contains applications of the subinaccessible cardinals apparatus and its basic tools - theories of reduced formula spectra and matrices, disseminators and others, which are used here in this proof and are set forth now in their more transparent and refined form. Much attention is devoted to the more explicit and substantial development and cultivation of basic ideas, serving as grounds for all main constructions and reasonings. The proof of the theorem about inaccessible cardinals nonexistence is presented in its detailed exposition. Several easy consequences of this theorem and some well-known results are presented. Appropriated for specialists in Set Theory and Mathematical Logic, and also for teachers and students of faculties of the mathematical profile.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

↑